Question

To estimate the mean score of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about . You want your sample mean to estimate with an error of no more than point in either direction. (a) What standard deviation must have so that of all samples give an within point of ? Use the rule. (Enter your answer rounded to four decimal places.)

Answer 1

Answer:

Given

(a) To estimate the mean score of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students.

Here to consider sample standard deviation(s)=6.6

To find the standard deviation must x bar have so that 99.7% of all samples give an x bar within 1.1 point of $\mu$ ?Use the 68-95-99.7 rule:

The 68-95-99.7 rule is also known as the empirical rule,three sigma states that nearly all values are lie within three standard deviation of the mean in a normal distribution.

Therefore,

P($\mu$-3$\sigma$<x<$\mu$-3$\sigma$) = 99.7/100

P($\mu$-3$\sigma$<x<$\mu$-3$\sigma$) = 0.997

3$\sigma$=1.1

$\sigma$=1.1/3

=0.3667

Hence the standard deviation of x bar is  $\sigma$=0.3667

Now to find the sample size(n):

We know that

$\sigma$ =S/$\sqrt{}$n

  $\sqrt{}$n = S/$\sigma$

Now squarring on both sides then we get,

n = [6.6/0.3667]^2

n= 323.941

n= 324

Therefore, n= 324